Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20298946 | C2 | semidirect |
| 3. #20298922 | C2 | semidirect |
| 4. #20298880 | C2 | semidirect |
| 5. #20298829 | C2 | semidirect |
| 6. #20298798 | C2 | semidirect |
| 7. #20298758 | C2 | semidirect |
| 8. C4×#14268637 | C2 | semidirect |
| 9. D4×#11744751 | C2 | semidirect |
| 10. #20298592 | C2 | semidirect |
| 11. #556×C113 | C2 | semidirect |
| 128. C113 | #3304 | semidirect |
| 129. #556 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299269 | 2 |
| #20298946 | 2 |
| #20298922 | 2 |
| #20298880 | 2 |
| #20298829 | 2 |
| #20298798 | 2 |
| #20298758 | 2 |
| C4×#14268637 | 2 |
| D4×#11744751 | 2 |
| #20298592 | 2 |
| #556×C113 | 2 |
| #3304 | 113 |